Strange lines appearing when render Anisotropic BSDF
Here is the final fixed result:



Shading

You need to click on the Tangent menu in the material settings and select a Tangent node. Make sure Radial is selected it its settings. Play around with the Axes: to figure out which one to use.



Gandalf3's image from here.

Modeling

Your mesh is covered in triangles (not good). From the .blend file that I downloaded, this was my process:


A twice to select everything.
Alt + J converts many tris to quads.
Ctrl + Tab, then 3 to enter Face Select Mode.
Alt +  RMB while hovering over one of the edges around the outside rim to select this face loop:





Ctrl + I to Invert Selection.
X > Faces to open the Delete menu and delete Faces.
Ctrl + Tab, then 1 to enter Vertex Select Mode.
Alt +  RMB while hovering over one of the edges in the topmost edge loop to select this edge loop:





F to create an N-Gon face.
Ctrl + I to Invert Selection.
F to create an N-Gon face.
Tab out of Edit Mode.


Here is the fixed .blend file:



P.S.

This is not included in the .blend file, but if you want less spotty anisotropy, you should use these settings in the Properties panel > Render tab.



They produce this result: